Higher-order Laue Zone Research Articles

On the measurement of dislocation core periods by nanodiffraction

Abstract Multiple-scattering calculations are used to demonstrate that the periodicity of dislocation cores may be measured from coherent convergent beam patterns obtained using a subnanometre probe with the electron beam aligned with the dislocation core. The resulting ‘half-order’ high-order Laue zone ring which results from a double-period core reconstruction is shown to be detectable above the background of thermal diffuse scattering. Multiple-scattering calculations which include thermal scattering are used to show the temperature and thickness dependences of this ring. Activation energies for core processes may be obtained by this method.

Lattice Strain around Platelet Oxide Precipitates in C- and N-Doped Silicon Epitaxial Wafers

The effect of heavy C and N doping on local lattice strain around platelet oxide precipitates in Czochralski silicon substrates of p/p− epitaxial (epi) wafers was investigated quantitatively using convergent beam electron diffraction (CBED). C- and N-doped p/p− epi wafers, including platelet precipitates with an edge length of approximately 500 nm, were prepared with an isothermal annealing at 800°C for 700 h. The results of strain analysis were compared with the reported results of polished wafers and heavily B-doped epi wafers, including an almost equal platelet density and length to C- and N-doped epi wafers. It was found, with strain analysis from high order Laue zone patterns in the CBED disk, that (i) the type of lattice strain in C- and N-doped epi wafers was coincided to polished and B-doped epi wafers. The strain along the normal direction to the flat plane of the platelet precipitate was compressive, while the strain along the parallel direction to the flat plane of the platelet was tensile; (ii) the strain in C-doped epi wafers was as large as that in B-doped epi wafers, and far relaxed compared with N-doped epi and polished wafers. Since the substitutional carbon concentration did not change during the isothermal annealing, the strain relaxation in C-doped epi wafers was caused by the availability of effective sinks in the matrix for silicon interstitials emitted by the precipitates. © 2001 The Electrochemical Society. All rights reserved.

HOLZ line analysis of lattice parameters in magnesium alloys.

A method of refining lattice parameters from deficit higher-order Laue zone (HOLZ) line data from large angle convergent beam electron diffraction (LACBED) data is presented, relying on distances between nearest neighbour intersections alone in order to minimize effects of distortion over the field of view. Use is made of a dynamical correction deltak to the fast electron wavevector k for kinematic analysis. This correction term is shown to depend on the specific HOLZ beam under consideration, as well as the zone axis and eigenvalue associated with the branch index of the relevant dispersion surface. This method is applied to analysis of data from magnesium alloys, where momentum filtering induced by the LACBED method facilitates HOLZ contrast from a relatively low index zone axis (where contrast is not detectable with conventional CBED), and contrast is enhanced at elevated temperatures from a higher index zone axis. Although the accuracy of refined lattice parameters from these sets of data is shown to be no better than 0.1%, it is felt that issues arising out of the analysis may be of some interest, particularly since these are non-ideal specimens. Full eigen-state analysis of the fast electron wavefunction is presented, and issues related to the influence of the dispersion surface on deficit HOLZ line behaviour are discussed.

Higher‐order Laue zone line contrast in large‐angle convergent‐beam electron diffraction around a dislocation

The physical picture of higher-order Laue zone (HOLZ) line contrast in a large-angle convergent-beam electron diffraction pattern around a dislocation, which is used for determining the Burgers vector, was examined. To evaluate the analytical expression of diffracted wave amplitude, we introduced an approximate form of the atomic displacement field of a dislocation. We showed that the four features of the HOLZ line contrast, that is, splitting, fading, bending and periodical contrast can be explained by analysis of the atomic displacement field. The localized lattice plane bending around a dislocation core made a HOLZ line split, fade and bend. However, we found that the periodical contrast of a HOLZ line was produced by the change of phase difference of the atomic displacement field between the crystals above and below the slip plane across the dislocation line.

An investigation of strain fields in dispersion strengthened aluminium by convergent beam electron diffraction

Dispersion strengthened aluminium was investigated in the as-produced, annealed and deformed states by convergent beam electron diffraction. The positions of the higher-order Laue zone (HOLZ) lines were determined by applying a Hough transform. Kinematic simulations were used for comparison with the experimental images, where the HOLZ line positions were individually corrected to account for the dynamic line shifts. Lattice parameters were derived by an iterative algorithm based on that of Rozeveld and Howe. It is demonstrated that the solutions are not unique, but instead belong to a manifold of equivalent lattice parameter sets of dimension two or higher. On a semi-quantitative basis, the results show long-range strain fields to be present inside the aluminium grains, explaining the peculiar mechanical behaviour of the material. The correlation between the strain fields and the observed dislocation networks is discussed.

Measurement of service-induced internal elastic strains in a single-crystal nickel-based turbine blade with convergent-beam electron diffraction

Abstract During tensile creep deformation, single-crystal nickel-based superalloys develop a characteristic internal stress state, which leads to counteracting tetragonal lattice distortions of the two phases γ and γ'. The aim of this work was the evaluation of the related elastic lattice distortions in the microstruture of a turbine blade after service in an accelerated mission test with high lateral resolution by convergent-beam electron diffraction. For the determination of the local lattice parameters, the higher-order Laue zone (HOLZ) lines of the central diffraction disc were evaluated under the assumption of a tetragonal distorted crystal lattice. The zone-axis patterns were simulated considering dynamical effects of the diffraction process. In order to reduce the computation time, a set of HOLZ line patterns was calculated in advance. Experimental patterns were compared with dynamically simulated patterns by the analysis of characteristic areas between HOLZ lines. The dependence of two area fractions on the lattice parameters were fitted by an interpolation function. This function was used for the evaluation of the experimental patterns. With this new approach a relatively fast evaluation of lattice strains was possible.

Nanometer Crystal Structure Analysis by EF-CBED and EF-Microscopy

Abstract Crystal structure refinement by the convergent-beam electron diffraction (CBED) method has the following advantages: (i) Nanometer-size crystal structure refinement: CBED patterns can be obtained from specimen areas of a few nanometer in diameter, (ii) Dynamical diffraction effect: the CBED intensities contain phase information of crystal structure factors through the strong dynamical effect. (iii) Site-selective analysis: the use of Bloch states formed by incident electrons allows structure determination weighted for specific atom sites. Energy-filtering (EF) to revome inelastically scattered background is now getting necessary for such quantitative analysis of CBED patterns. Especially for the determination of atom positions and Debye-Waller factors, the use of energy-filtered higher-order Laue zone (HOLZ) CBED patterns is essential because small displacements of atoms can be sensitively detected using HOLZ reflections with large reciprocal vectors. For this purpose, we developed a new fl-filter transmission electron microscope (JEM-2010FEF) with a high acceptance angle [2] and a new analysis program “mbfit” to refine structural parameters using many-beam Bloch-wave calculations and least-square fitting [1].

Atomic site occupancy in D022and L12titanium trialuminides

Abstract X-ray incoherent channelling patterns (ICPs) are generated by variations in characteristic X-ray emission rates induced by a systematic scan of incident fast electron beam orientation near low index zone axes. ICP contrast is used to derive relative sublattice site occupancies of alloyed atoms in Al3Ti and related intermetallics. Depending on composition and alloying atoms, these have crystal structures of type D022 or L12. When V is added to form the D022 intermetallic A13(V0.6Ti0.4), it is shown that Ti and V share the same sublattice site. The L12 structure is stabilized by additions of Cr (which induces the transformation from the D022 structure and stabilizes the L12 phase). Elements X = Hf, Zr and W were added at the 0.5at.% level to form separate quaternary alloys of overall composition A162Cr10.5Ti27X0.5 with the L12 crystal structure. The sublattice site partitioning of these minority atoms is investigated by the formation of X-ray ICPs and subsequent statistical analysis of these patterns, related to atom location by channelling enhanced microanalysis (or ALCHEMI). It is shown that Hf and Zr are accommodated exclusively on Ti sublattice sites whereas W favours the A1 sublattice site with about 10% of the alloyed W atoms accommodated on Ti sublattice sites. Cr is shown to partition exclusively onto the A1 sublattice site. Contrast from a 〈110〉 zone confirms that these minority atoms do not occupy the interstitial site at the body centre position of the L12 unit cell. Convergent beam electron diffraction data from the zero-order Laue zone and higher order Laue zone are shown and discussed for the 〈110〉 projection of the L12 structure.

Effect of heavy boron doping on the lattice strain around platelet oxide precipitates in Czochralski silicon wafers

The effect of heavy boron doping on local lattice strain around platelet oxide precipitates in Czochralski silicon wafers was investigated quantitatively by convergent beam electron diffraction (CBED). Lightly boron doped (p−) polished wafers, including platelet precipitates with density of about 5×109/cm3 and with an edge length of about 500 nm, were prepared with an isothermal annealing at 800 °C for 700 h. Heavy boron doped (p/p+) epitaxial wafers, including an almost equal precipitate density and length to p− wafers, were also prepared with an isothermal annealing at 800 °C for 200 h. It was found by strain analysis from high-order Laue zone patterns in the CBED disk that (i) the type of lattice strain was coincident in p− and p/p+ wafers: the strain along the normal direction of the platelet precipitate was compressive, while the strain along the parallel direction of the platelet was tensile; (ii) the strain in p/p+ wafers was smaller than that in p− wafers; and (iii) the punched-out dislocations were generated by platelets only in p− wafers. The results of (ii) and (iii) indicate that the strain around the platelets is relaxed due to the heavy boron doping.

A dynamical Bragg equation for high-order Laue zone reflections

A dynamically corrected Bragg equation for high-order Laue zone (HOLZ) reflections is derived directly from the Bloch wave formalism instead of the geometric argument used to deduce the kinematical Bragg condition. It differs from the kinematical Bragg equation by replacing the plane wave vector in the kinematical equation with the Bloch wave vectors. This dynamical equation reduces to the kinematical equation when the crystal potential is zero. It also demonstrates the occurrence of dynamical shifts for the HOLZ reflections but their absence for the zero-order Laue zone (ZOLZ) reflections in the symmetrical Laue case.

Analysis of local strain in aluminium interconnects by energy filtered CBED

Energy filtered convergent beam electron diffraction (CBED) was used to investigate localised strain in aluminium interconnects. The quantitative analysis of the experimental patterns is based on a multi-step evaluation procedure which is the main subject of the present paper. The improvements which were made to the analysis method aim at increasing both the automation and the accuracy. The detection of the higher order Laue zone (HOLZ) line positions is performed by means of the Hough transform. The required sub-pixel resolution can be achieved routinely and the achievable accuracy is only limited by the line width and the amount of noise in the patterns. The determination of the strain state is performed via a refinement algorithm which is based on varying the strain state in the sample coordinate system and simulating the patterns for the individual grains until a best fit with the experiment is obtained. For the simulation we have developed a new correction scheme in which the dynamical effects are treated separately for each individual HOLZ line. The results show that the main source of the observed strains is the difference in thermal expansion coefficients. The strain is substantially reduced underneath a hillock in the interconnect. Asymmetries in the strain distribution around the hillock show that the unidirectional diffusion during electromigration tests causes peak strains in areas next to the hillock which may be possible failure sites.

Local lattice strain measurements in semiconductor devices by using convergent-beam electron diffraction

We examined the lattice strain distribution around local oxidation of silicon (LOCOS) in a semiconductor device by using highly accurate (1.8×10 −4 standard deviation) convergent-beam electron diffraction (CBED) at a nanometer-scale spatial resolution (10 nm in diameter). The nanometer-scale measurement was done by reducing the elastic relaxation using a thick (about 600 nm) sample and by removing the inelastically scattered electrons by means of an electron energy filter. A highly accurate measurement was achieved through the analysis of higher-order Laue zone (HOLZ) patterns using the least-squares fitting of HOLZ line intersection distances between the observations and calculations. Our examination showed that the LOCOS structure gave singularities in strain distributions at the field edge. That is, compressive strain exists in both the vertical and horizontal directions of the substrate, and the shear strain increased there. Most notably, two-dimensional measurements revealed that the singularity of the normal strain in the horizontal direction of the substrate generated at the field edge propagated into the substrate.

Use of reciprocal lattice layer spacing in electron backscatter diffraction pattern analysis

In the scanning electron microscope using electron backscattered diffraction, it is possible to measure the spacing of the layers in the reciprocal lattice. These values are of great use in confirming the identification of phases. The technique derives the layer spacing from the higher-order Laue zone rings which appear in patterns from many materials. The method adapts results from convergent-beam electron diffraction in the transmission electron microscope. For many materials the measured layer spacing compares well with the calculated layer spacing. A noted exception is for higher atomic number materials. In these cases an extrapolation procedure is described that requires layer spacing measurements at a range of accelerating voltages. This procedure is shown to improve the accuracy of the technique significantly. The application of layer spacing measurements in EBSD is shown to be of use for the analysis of two polytypes of SiC.

Measurement of Local Lattice Parameter in Ion-Implanted Silicon Using HOLZ Lines

A simple algorithm based on a dynamical fitting simulation of higher-order Laue zone (HOLZ) lines is demonstrated, which presents a profile of lattice parameter with a spatial resolution of several nanometers. The proposed procedure is tested on arsenic ion-implanted silicon, being shown to be appreciable to accurate determination of lattice parameter by selecting a weak zone axis with any restriction. By comparing with the arsenic distribution, the small lattice elongation observed beneath the ion-implanted surface is due to AsmVn complexes and the small increase beneath the amorphous–crystalline interface due to self-interstitials or their complexes

Strain-induced symmetry breakdown in HOLZ lines from L12 titanium tri-aluminides

Energy filtered CBED patterns of the Cr-stabilized L1(2) phase of a titanium tri-aluminide alloy reveal deficit higher order Laue zone (HOLZ) lines in the zeroth order diffraction disk, for which the expected 4-mm symmetry is significantly broken in the <001> projection. This apparent break of symmetry may be explained by the presence of lattice strains of order 10(-3). Effects of strain-induced lattice distortions on HOLZ line symmetries are calculated by an introduction of rhombohedral, tetragonal or monoclinic distortions to the cubic unit cell. It is shown how tensile and shear components of strain affect the overall HOLZ line symmetries in different ways.

Localized Measurement of Strains in Damascene Copper Interconnects by Convergent-Beam Electron Diffraction

AbstractConvergent beam electron diffraction (CBED) was used to measure localized lattice strains in damascene copper interconnects. This method provides data from areas of approximate diameter 20 nm, enabling evaluation of strain states within individual grains. Lattice parameters were determined by measuring the deficient higher order Laue zone (HOLZ) line positions in experimental zone axis patterns and subsequently comparing them to kinematical and dynamical simulations. Quantitative comparison was accomplished using a least squares analysis of distances between line intersections. Deposition-induced strains between 0.06% and 0.14% were measured in 2.0 µm wide lines. The uncertainty in strain determination was approximately 0.02%, as limited by the precision in HOLZ line detection. In addition to enabling localized analysis of strain states, another advantage of using CBED is that the microstructure can be fully evaluated. Used in conjunction with global methods such as X-ray diffraction, CBED may provide unique insight into localized failure phenomena such as electromigration void formation in damascene copper.

Refinement of crystal structural parameters using two-dimensional energy-filtered CBED patterns.

A new method to refine crystal structural parameters using convergent-beam electron diffraction (CBED), which is applicable to nanometre-size crystal structure analysis, is proposed. This method is based on the fitting between theoretical calculations and experimental intensities of energy-filtered two-dimensional CBED patterns containing higher-order Laue-zone (HOLZ) reflections. The use of HOLZ reflections is essential for the method because small displacements of atoms can be sensitively detected using HOLZ reflections with large reciprocal vectors. For this purpose, a new Omega-filter transmission microscope (JEM-2010FEF), which can take energy-filtered CBED patterns up to a high angle with a small distortion, and a new analysis program to refine structural parameters, which is based on many-beam Bloch-wave calculations and nonlinear least-squares fitting, have been developed. As a test example, a positional parameter and isotropic and anisotropic Debye-Waller factors of CdS have been refined. Two-dimensional CBED patterns calculated with the refined parameters show very good agreement with the experimental ones, and the refined values of the parameters also agree well with the result of a single-crystal X-ray diffraction experiment. Important problems of the analysis procedure are discussed item by item.

Determination of lattice parameter, oxidation state, and composition of individual titanomagnetite/titanomaghemite grains by transmission electron microscopy

A transmission electron microscopy (TEM) method, higher‐order Laue zone (HOLZ) diffraction, has been applied to measurement of accurate lattice parameters of individual titanomagnetite and titanomaghemite grains. Lattice parameters and cation‐composition data are obtained with TEM/analytical electron microscopy (AEM) for individual grains smaller than 0.1 μm in diameter. A suite of Ocean Drilling Program/Deep Sea Drilling Project ocean‐floor basalts containing titanomagnetite‐titanomaghemite with a wide range of oxidation degree (z), were employed to establish the relationship between lattice parameter (a), z and Ti‐content (x) for naturally occurring samples. Standardization was accomplished with measurements on grains sufficiently large to allow the determination of absolute oxygen contents by electron microprobe analyses, which directly yielded z values. The probe data confirm that the maghemitization process in ocean‐floor basalts is one involving loss of iron and indicate a nearly linear relationship between lattice parameters and oxidation degrees for a given x value, except for the smallest and largest values of z. The standardized relation permits determination of z for individual submicrometer‐sized grains using only measured a‐values and cation compositions as determined by HOLZ diffraction and AEM.

CBED Investigations of Mesoscopic Semiconductor Structures

Abstract Ternary and quaternary heterostructures from III-V-semiconductors get more and more importance in the fabrication of high-speed/high frequency devices in telecommunication systems. One of the key parameters for the performance of such devices is the crystalline quality and especially the amount of tetragonal distortion in strained layers on a nanometer scale. Strain can cause problems for the growth of such layers like relaxation induced defects, especially for the case of a high value of lattice mismatch. However, strain and the associated influence on the band structure can be used consciously for the design of tailor-made heterostructures (band gap engineering). Therefore, the spatially resolved investigation of local crystal properties (tetragonal distortion or strain and strain relaxation) is a key tool for the characterization of strained layers. Convergent beam electron diffraction (CBED) patterns and convergent beam imaging (CBIM) can be used to evaluate informations on the local crystalline structure. E.g. the position of the High Order Laue Zone (HOLZ) lines in the CBED patterns is sensitive to the local strain and therefore can be used to determine strain and relaxation effects in heterostructures quantitatively. But in practice the applicability of CBED is often limited by a lack of ultimate spatial resolution and/or of sensitivity.

Analysis of Local Lattice Strain Around Oxygen Precipitates in Czochralski-Grown Silicon Wafers Using Convergent Beam Electron Diffraction

The local lattice strain field around oxygen precipitates in Czochralski-grown silicon (CZ-Si) wafers has been measured quantitatively using convergent beam electron diffraction (CBED). As a result of the strain analysis from higher-order Laue zone patterns in the CBED disk, strain of the silicon lattices was found in the vicinity of oxygen precipitates, i.e., platelet type and polyhedral type. The strain along the normal direction to the precipitate is compressive, and the strain along the parallel direction to the precipitate is tensile. The lattice strain field around the precipitate decreases monotonically as a function of distance from the precipitate/matrix interface. Further, the morphological change in the growth process of the precipitate is important for the formation of the local lattice strain.